1. Field of the Invention
This invention relates in general to a rotatable storage systems, and more particularly to a method and apparatus for reducing track misregistration due to digital-to-analog converter quantization noise.
2. Description of Related Art
Rotatable disk data storage systems are widely used in computer systems to provide rapid data file access for reading and writing. These rotating data storage systems include disk memory media using servo-actuator driven transducer assemblies that are driven by voice coil motors (VCM) to access rotating platters. Rotating disk storage systems also include optical disk memory employing a laser read-write head assembly to access optical disks.
The reading and writing information to the concentric data tracks in a rotating storage device is subject to data errors arising from head tracking errors that occur during data storage to the file and during data retrieval from the files. For example, one method known in the art for reducing both hard and soft errors during writing and reading from a storage disk is to define a track centerline and establish limited offtrack regions about each track centerline on the disk. The offtrack method provides a threshold measure for inhibiting the read or write functions of the head assembly. That is, the write function is inhibited (disabled) when the head position exits the offtrack regions.
Nevertheless, in hard disk drives (HDD), the digital to analog converter (DAC) driving the voice coil motor (VCM) has limited accuracy. Quantization noises (or roundoff errors) due to the finite precision of the DAC can disturb the servo control loop and degrade servo performance. In the digital servo control loop, the internal precision of the digital signal processor (DSP) is typically higher (e.g., 16 bits) than that of the DAC (e.g., 12 bits). As a result, the lower order bits have to be dropped when the calculated control signal is sent to the DAC. This dropping of the lower order bits, i.e., the DAC quantization noise, may contribute a significant portion of the total track-misregistration (TMR). Furthermore, for fixed mechanics and servo bandwidth in a HDD, the power spectrum of TMR due to DAC noises is fixed, and the TMR does not scale with the track density.
It can be seen then that there is a need for a method that effectively reduces TMR due to DAC quantization noise.
To overcome the limitations in the prior art described above, and to overcome other limitations that will become apparent upon reading and understanding the present specification, the present invention discloses a method and apparatus for reducing track misregistration due to digital-to-analog converter quantization noise.
The present invention solves the above-described problems by providing a quantization error feedback method that compensates for the dropping of lower order bits from a processor to a digital-to-analog converter driving a plant.
A method in accordance with the principles of the present invention includes providing control signals for controlling a plant, the control signals each having a precision of a first predetermined number of bits further comprising a first group of most significant bits and at least one least significant bit, providing each of the first group of most significant bits to the plant to control operation of the plant, accumulating the at least one least significant bit until a new most significant bit is generated and adding the new most significant bit to a first group of most significant bits before being provided to the plant.
Other embodiments of a method in accordance with the principles of the invention may include alternative or optional additional aspects. One such aspect of the present invention is that the accumulating the at least one least significant bit until a new most significant bit is generated further comprises feeding the at least one least significant bit through a feedback loop having a feedback loop gain until the new most significant bit is generated.
Another aspect of the present invention is that feedback loop gain is zxe2x88x921 F(z), where F(z) is a filter whose transfer function is assumed to be a real rational function which is analytic and bounded in {z:∥z∥xe2x89xa71}.
Another aspect of the present invention is that the feedback loop gain is a single integrator.
Another aspect of the present invention is that the feedback loop gain is a double integrator.
Another aspect of the present invention is that the filter F(z) provides a power spectrum SGQE(xcfx89) of shaped noise that always satisfies                     1        π            ·                        ∫          0          π                ⁢                              ln            ⁡                          (                                                S                  GQE                                ⁡                                  (                  ω                  )                                            )                                ⁢                      ⅆ            ω                                =    K    ,
where K is a constant.
Another aspect of the present invention is that the control error is track misregistration, the track misregistration being measured according to a position error signal (PES), the mean square value of PES satisfying             E      ⁡              (                              PES            2                    ⁡                      (            t            )                          )              ≥                            q          2                12            ·              h        0        2              ,
where q=2lc with c being the quantization resolution in the processor, and l being a number representing the at least one least significant bit.
Another aspect of the present invention is that the control error is track misregistration, the track misregistration being measured according to a position error signal (PES), a minimum of the mean square value of PES being derived according to a method including constructing state space matrices B2, D2, A, and B, solving ALATxe2x88x92L+BBT=0 to get the solution       L    =          [                                                  L              11                                                          L              12                                                                          L              21                                                          L              22                                          ]        ,
finding the optimal filter coefficients: f*=C2L12L11xe2x88x921 and solving for the minimum of the mean square value of PES given by:             min      f        ⁢          E      ⁡              (                              PES            2                    ⁡                      (            t            )                          )              =                    q        2            12        ⁢                  (                                                            C                2                            ⁡                              (                                                      L                    22                                    -                                                            L                      12                                        ⁢                                          L                      11                                              -                        1                                                              ⁢                                          L                      21                                                                      )                                      ⁢                          C              2              T                                +                      h            0            2                          )            .      
Another aspect of the present invention is that the mean square value of PES achieves the lower bound,                     q        2            12        ·          h      0      2        ,
by additionally feeding forward the filtered QEF noise QN to the controller input when there is at least one sampling delay in the servo loop.
Another aspect of the present invention is that the method further includes driving a state estimator with the most significant bits and a position error signal to reduce the power spectrum density function of the track misregistration at predetermined frequencies. The quantization error feedback method and the state estimator method may be used separately, or alternatively, may be used jointly to achieve even more track misregistration than if either is used separately.
In another embodiment of the present invention the method includes providing control signals for controlling a plant, the control signals each having a precision of a first predetermined number of bits further comprising a first group of most significant bits and at least one least significant bit and driving a state estimator with the most significant bits and a position error signal to reduce the power spectrum density function of the track misregistration at predetermined frequencies.
These and various other advantages and features of novelty which characterize the invention are pointed out with particularity in the claims annexed hereto and form a part hereof. However, for a better understanding of the invention, its advantages, and the objects obtained by its use, reference should be made to the drawings which form a further part hereof, and to accompanying descriptive matter, in which there are illustrated and described specific examples of an apparatus in accordance with the invention.